Northrop Frye's theory of four fundamental narrative genres (comedy, romance, tragedy, satire) has profoundly influenced literary criticism, yet computational approaches to his framework have focused primarily on narrative patterns rather than character functions. In this paper, we present a new character function framework that complements pattern-based analysis by examining how archetypal roles manifest differently across Frye's genres. Drawing on Jungian archetype theory, we derive four universal character functions (protagonist, mentor, antagonist, companion) by mapping them to Jung's psychic structure components. These functions are then specialized into sixteen genre-specific roles based on prototypical works. To validate this framework, we conducted a multi-model study using six state-of-the-art Large Language Models (LLMs) to evaluate character-role correspondences across 40 narrative works. The validation employed both positive samples (160 valid correspondences) and negative samples (30 invalid correspondences) to evaluate whether models both recognize valid correspondences and reject invalid ones. LLMs achieved substantial performance (mean balanced accuracy of 82.5%) with strong inter-model agreement (Fleiss' $κ$ = 0.600), demonstrating that the proposed correspondences capture systematic structural patterns. Performance varied by genre (ranging from 72.7% to 89.9%) and role (52.5% to 99.2%), with qualitative analysis revealing that variations reflect genuine narrative properties, including functional distribution in romance and deliberate archetypal subversion in satire. This character-based approach demonstrates the potential of LLM-supported methods for computational narratology and provides a foundation for future development of narrative generation methods and interactive storytelling applications.